A101681 Numbers k such that gcd(C(2k,k), 2k+1) > 1.

7, 16, 17, 19, 22, 25, 31, 34, 38, 42, 43, 45, 46, 47, 49, 52, 55, 58, 61, 64, 67, 70, 71, 72, 73, 76, 77, 79, 80, 82, 87, 88, 92, 93, 94, 97, 100, 102, 103, 104, 106, 107, 110, 112, 115, 117, 122, 123, 124, 127, 129, 130, 133, 136, 139, 142, 143, 145, 147, 148

Offset: 1

Author

Ralf Stephan, Dec 11 2004

Keywords

• nonn

Comments

Positions where A056616 differs from A000984.

The set seems to have greater cardinality than its complement.

Positions where A055786 differs from A001790. - Mohammed Yaseen, Aug 03 2024

Examples

			7 is in the sequence as gcd(binomial(2*7, 7), 2*7 + 1) = gcd(3432, 15) = gcd(3*1144, 3*5) > 1. - _David A. Corneth_, Apr 03 2021
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000984, A056616, A126786.

Programs

Mathematica

Select[Range[200],GCD[Binomial[2 #,#],2 #+1]>1&] (* Harvey P. Dale, May 11 2019 *)

PARI

is(n) = { my(f = factor(2*n+1)); for(i = 1, #f~, if(val(2*n, f[i, 1])-2*val(n, f[i, 1]) > 0, return(1))); 0 }
val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Apr 03 2021